Cologne, Germany

I stayed at the City Class Europa am Dom hotel, which was a short distance from the train station. It was a wonderful location and I had a view of the cathedral from my window. The hotel was quite nice, a reasonable price, very clean, with a good breakfast (not included but available). I enjoyed my stay here very much. I think that area, regardless of which hotel you choose, is a very convenient place to stay.

Can't say as for a hotel, but for NYE get your party boat tickets now before they sell out. they usually board around 8pm and park in the middle of the river for the best fireworks views. Get one with open bar and food.

Thanks so much for your response! Do you have the name of a boat/company that you recommend?

I would want a back or courtyard room for NYE. We stayed at the relatively expensive Hilton. Note that Cologne is exceptionally walkable (winter wind aside) from the HBF. U-Bahn needed only for Medieval and Ethnographic museums.

I have not been to anything like Rhine In Flames or NYE. But partying aside, the Rhine in Cologne is modern, not historic or scenic.

When I was in Cologne last December I stayed at the Marriott, which was conveniently located to the train station. It was reasonably priced, though you may have to pay a premium anywhere over New Years. I hope you have a great trip.
https://www.marriott.com/en-us/hotels/cgnmc-cologne-marriott-hotel/overview/

I can't recommend a specific company, as they all offer multiple choices of food, and music. Some leave earlier than other, some actually go up or down river for a couple hours; you'll have to google and sort out what you'd be interested in. The boats all basically come together before the fireworks start; their spaces are allocated by the river traffic comptrollers. I'd book a hotel ASAP as Koln is very popular for NYE.

If you were staying longer I'd suggest taking the train an hour south to Koblenz and hitting their Christmas Market and the Winter Garder at the fortress. https://www.christmas-garden.de/koblenz/

https://www.koeln.de/silvester/silvester-schiff-koeln/

I have no experience of New Year's Eve celebrations in Cologne. However, if you're not celebrating outdoors, I could well imagine that you definitely have to reserve seats. Regardless of whether it's a party, restaurant, etc.
Please take good care of your daughters, especially around the Cologne train main station. Unfortunately, there have already been major problems there. However, the police presence is said to have improved. Hope, I remembered right about this information.

I'm sure the city will be unusually safe this New Year's Eve given the 2015-2016 incidents.
https://en.wikipedia.org/wiki/2015%E2%80%9316_New_Year%27s_Eve_sexual_assaults_in_Germany